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Types of Numbers

Types of Numbers

At a Glance - How to Solve a Math Problem

How to Solve a Math Problem

Shouldn't we have started out with this? Oh, it's no big deal. You already know how to do all this business. It's just a little review of the general process, so this should all feel like old hat to you.

There are three steps to solving a math problem.

1. Figure out what the problem is asking.
2. Solve the problem.
3. Check the answer.

Simple enough.

Sample Problem

Doug went to the grocery store. He bought a bunch of bananas for $1.37 and a jar of peanut butter for $2.99. There was no tax (because he lives in the state of Simplified Math Problems—it's near North Dakota), and he paid with a ten-dollar bill. How much change will he get?

Let's work through the steps.

1. Figure out what the problem is asking.

We want to know how much change Doug will get. In other words, if he starts with $10, spends $1.37, and then spends $2.99, how much will he have left? He wants to know so that he's clear about how much he'll have to blow on scratchers.

2. Solve the problem.

There are two ways to write this word problem as an arithmetic problem. We can write:

$10 – ($1.37 + $2.99)


$10 – $1.37 – $2.99

Either way, Doug gets $5.64 in change. That'll get him five $1 scratchers, and he'll still have a bit left for laundry money. You go, Doug.

3. Check the answer.

We can check to see if the answer is reasonable or in the right ballpark by estimating. $1.37 is about $1.40, and $2.99 is about $3, so our answer should be about $10 – $4.40 = $5.60. Yep, $5.64 is indeed close to $5.60, which means our answer is probably right on the money.

We can also check to see that our answer is absolutely, perfectly correct by working backwards. In this case, the cost of the bananas plus the cost of the peanut butter plus the change should add up to $10.00. So $1.37 + $2.99 + $5.64 should equal $10.00, which it does. Weird. We just totally got a taste for banana peanut butter sandwiches. Wonder where that came from.

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